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Simplifying 7k2 + 11k + 29 = -3k Reorder the terms: 29 + 11k + 7k2 = -3k Solving 29 + 11k + 7k2 = -3k Solving for variable 'k'. Reorder the terms: 29 + 11k + 3k + 7k2 = -3k + 3k Combine like terms: 11k + 3k = 14k 29 + 14k + 7k2 = -3k + 3k Combine like terms: -3k + 3k = 0 29 + 14k + 7k2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4.142857143 + 2k + k2 = 0 Move the constant term to the right: Add '-4.142857143' to each side of the equation. 4.142857143 + 2k + -4.142857143 + k2 = 0 + -4.142857143 Reorder the terms: 4.142857143 + -4.142857143 + 2k + k2 = 0 + -4.142857143 Combine like terms: 4.142857143 + -4.142857143 = 0.000000000 0.000000000 + 2k + k2 = 0 + -4.142857143 2k + k2 = 0 + -4.142857143 Combine like terms: 0 + -4.142857143 = -4.142857143 2k + k2 = -4.142857143 The k term is 2k. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2k + 1 + k2 = -4.142857143 + 1 Reorder the terms: 1 + 2k + k2 = -4.142857143 + 1 Combine like terms: -4.142857143 + 1 = -3.142857143 1 + 2k + k2 = -3.142857143 Factor a perfect square on the left side: (k + 1)(k + 1) = -3.142857143 Can't calculate square root of the right side. The solution to this equation could not be determined.
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